Introduction to Hadronic Final State Reconstruction in Collider Experiments (Part X)

1. Introduction to Hadronic Final State Reconstruction in Collider Experiments(Part X) Peter Loch University of Arizona Tucson, Arizona USA

2. Calorimeter Signal Definitions • Need to have another look at the calorimeter • Basically all calorimeters at collider experiments show some level of non-compensation • For sure the ones in ATLAS and CMS are! • Needs to be corrected for jet calibration • And all other hadronic final state contributions like isolated hadrons, tau-leptons, and low pThadronic signals • Can this be done for highest spatial calorimeter granularity (cells)? • Not easy to see – individual cell signal without any other context hard to calibrate in non-compensating calorimeters • Better to establish a larger context first to find out which calibration the calorimeter cell signal needs • Reconstructed jet itself – in ATLAS this is called Global Calibration • Topological cell clusters without jet context – in ATLAS this is called Local Calibration • Cannot recommend to use cells directly to find jets: • High multiplicity on input for jet finders • Negative signal treatment required for four-momentum recombination • Noise can create E<0 in cells • Jets should consistent of significant (relevant) signal objects • Cell signal not a good image of the particle flow in jets • Larger calorimeter signal objects clearly preferred • Towers of cells – add cell signal up in projective calorimeter towers • Topological clusters of cells – add cell signals following signal correlations in showers

3. Calorimeter Towers

4. Calorimeter Towers

5. Calorimeter Towers: Sum Rules • Impose a regular grid view on event • Δ×Δφ = 0.1×0.1 grid • Motivated by particle Et flow in hadron-hadroncollisions • Well suited for trigger purposes • Collect cells into tower grid • Cells signals can be summed with geometrical weights • Depend on cell area containment ratio • Weight = 1 for projective cells of equal or smaller than tower size • Summing can be selective • Noise filter can be applied to cell signals! • Towers have massless four-momentum representation • Fixed direction given by geometrical grid center projective cells non-projective cells

6. More On Calorimeter Towers • Signal integration • Towers represent longitudinally summed cell signals • 2-dimensional signal objects • Can include partial and complete signals from several particles • Towers can preserve more detailed signal features • Associated information to be collected at tower formation • E.g., energy sharing in electromagnetic and hadronic calorimeters • Longitudinal signal center of gravity • Signal splitting • Towers can split signal from single particles • Hadronic shower width can be larger then tower bin, especially at higher pseudo-rapidity • Can cause problems with infrared safety • Can cause problems for seeded jet finders • Collateral instability • Can lead to lost signals cone-like jets • Energy in tower bins outside of jet can belong to particle signal in jet (drawing by K. Perez, Columbia University) Unbiased calorimeter tower is a “slab” of energy in a regular pseudorapidity-azimuth grid (each tower covers the same area in these coordinates)

7. Topological Cell Clusters • Collect cell into energy “blobs” • Idea is to collect all cell signals belonging to a given particle into one cluster of cells • Basically reconstruct the shower for each particle entering the calorimeter • Needs algorithm to form energy blobs at the location of the shower signal in the calorimeter • Follow the shower-induced cell signal correlations • Extract most significant signal from all calorimeter cells • Cluster formation uses signal significance as guidance • Not the total signal – noise changes from calorimeter region to calorimeter region • Implicit noise suppression in cluster formation • Cluster signals should include least amount of noise

8. Topological Cell Clusters Electronic Noise in Calorimeter Cells Pile-up Noise in Calorimeter Cells S. Menke, ATLAS Physics Workshop 07/2005 S. Menke, ATLAS Physics Workshop 07/2005 • Collect cell into energy “blobs” • Idea is to collect all cell signals belonging to a given particle into one cluster of cells • Basically reconstruct the shower for each particle entering the calorimeter • Needs algorithm to form energy blobs at the location of the shower signal in the calorimeter • Follow the shower-induced cell signal correlations • Extract most significant signal from all calorimeter cells • Cluster formation uses signal significance as guidance • Not the total signal – noise changes from calorimeter region to calorimeter region • Implicit noise suppression in cluster formation • Cluster signals should include least amount of noise

9. ATLAS Topological Cell Clustering • Cluster seeding • Defined by signal significance above primary threshold • Cells above this threshold can seed cluster • Cluster growth • Defined by signal significance above secondary threshold • Cells neighbouring seeds with significance above this threshold drive cluster growths • Cluster signal • Defined by cells with significance above basic threshold • Cells to be considered in cluster energy sums • Use of negative signal cells • Thresholds are considered for the absolute (unsigned) signal magnitude • Large negative signals can seed and grow clusters • Parameters for each stage optimized with testbeam data • Experimental single pion shower shapes guide cluster algorithm develpoment • Clean tuning reference! Famous “4/2/0” clustering in ATLAS

10. ATLAS Topological Cell Clustering  P  N  S  S  N  P • Cluster seeding • Defined by signal significance above primary threshold • Cells above this threshold can seed cluster • Cluster growth control • Defined by signal significance above secondary threshold • Cells neighbouring seeds with significance above this threshold drive cluster growths • Cluster signal • Defined by cells with significance above basic threshold • Cells to be considered in cluster energy sums • Use of negative signal cells • Thresholds are considered for the absolute (unsigned) signal magnitude • Large negative signals can seed and grow clusters • Parameters for each stage optimized with testbeam data • Experimental single pion shower shapes guide cluster algorithm develpoment • Clean tuning reference! Resolution of Sum Eclus 180 GeV pions Mean of Sum Eclus

11. Clustering Algorithms • Find cell with most significant seed over primary threshold S • Collect all cells with significance above basic threshold P • Consider neighbours in three dimensions • Defined by (partly) shared area, (partly) shared edge, or shared corner point • E.g., 26 neighbours for perfectly cubed volumes of equal size • Neighbours can be in other calorimeter regions or even other calorimeter sub-systems • Granularity change to be considered in neighbouring definition • For all cells neighbouring seeds with signal significance above secondary threshold N, collect neighbours of neighbours if their signal significance is above P • Same rules as for collection around primary seed • Continue until cluster does not grow anymore • Automatically generate “guard ring” of small signal cells at cluster margin • In three dimensions, of course • Take next not yet used seed cell and collect next cluster

12. Clustering Example

13. Clustering Example

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35. Clustering Example

36. Effect Of Strict Nearest Neighbour Approach • Large topologically connected regions in calorimeter can lead to large cell clusters • Lost particle flow structure can introduce problems for jets • Infrared safety, in particular • Need to refine the clustering algorithm • Try to match single particle shower shapes better • Splitting the clusters • Examine spatial cluster signal structure – find local signal maxima • “hill and valley” structural analysis in three dimensions • Split cluster between two maxima • In three dimensions, of course! • Share energy of cells in signal valleys • Needs sharing rules – introduces “geometrically” weighted cell energy contribution to cluster signal • Introduces new tunable parameter • Local signal maximum threshold is defined in units of energy, not significance!

37. Cluster Splitting

38. Cluster Splitting

39. Cluster Splitting

40. Splitting & Cell Energy Sharing • Splitting technique • Guided by finest calorimeter granularity • Typically in electromagnetic calorimeter • Allows to split larger cell signals without signal valley • Typically in hadronic calorimeters

41. Splitting & Cell Energy Sharing • Splitting technique • Guided by finest calorimeter granularity • Typically in electromagnetic calorimeter • Allows to split larger cell signals without signal valley • Typically in hadronic calorimeters

42. Cluster Shapes • Clusters have shapes • Geometrical moments and sizes • Lateral and longitudinal • Tilt of principal axis • With respect to direction extrapolation from primary vertex (magnetic field!) • Density and compactness measures • Cluster energy distribution in cells • Energy sharing between calorimeter segments and modules • Shower structures • Useful for cluster calibration • Exploit shape sensitivity to shower character • Hadronic versus electromagnetic

43. Cell Signal Significance Spectrum Modeled effect of topological clustering on the cell signal significance spectrum, for purposes of illustration here with only the primary (seed) threshold, no secondary (growth) threshold.

44. Cell Signal Significance Spectrum no clusters, cells with signal & noise

45. Cell Signal Significance Spectrum no clusters, cells with signal & noise no clusters, cells with only noise

46. Cell Signal Significance Spectrum no clusters, cells with signal & noise clustered cells, signal & noise no clusters, cells with only noise

47. Cell Signal Significance Spectrum no clusters, cells with signal & noise clustered cells, signal & noise no clusters, cells with only noise clustered noise cells

48. Cell Signal Significance Spectrum probability for “true” signal for clustered cells probability for “true” signal for all cells

49. Cell Signal Significance Spectrum probability for “true” signal for clustered cells probability for “true” signal for all cells Note change of shape of probability density function due to correlations introduced by showering – clustered small signal cells have more likely some true signal because they are in the neighbor-hood of a cell with significant signal, while cells with the same signal from noise only are more often suppressed!

50. Probably For Cell To Have True Signal Significant boost of likelihood that small signals are generated by particles (rather than noise) in clustered cells!